{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QGL4OM5AQSKYRDYST5A7B46IIM","short_pith_number":"pith:QGL4OM5A","canonical_record":{"source":{"id":"1007.0820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T07:11:07Z","cross_cats_sorted":[],"title_canon_sha256":"fa192292920f6a34e10250a75b4208883ebec66c151db7d9202794969febe5cc","abstract_canon_sha256":"fa513de4d0e54af60d43cfe06c1cf8b7c60c3bca38c85c4a3893bc46e2ff4726"},"schema_version":"1.0"},"canonical_sha256":"8197c733a08495888f129f41f0f3c84303f638d29e4b9824e15ead3f95ddbe11","source":{"kind":"arxiv","id":"1007.0820","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0820","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0820v1","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0820","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"QGL4OM5AQSKY","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QGL4OM5AQSKYRDYS","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QGL4OM5A","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QGL4OM5AQSKYRDYST5A7B46IIM","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T07:11:07Z","cross_cats_sorted":[],"title_canon_sha256":"fa192292920f6a34e10250a75b4208883ebec66c151db7d9202794969febe5cc","abstract_canon_sha256":"fa513de4d0e54af60d43cfe06c1cf8b7c60c3bca38c85c4a3893bc46e2ff4726"},"schema_version":"1.0"},"canonical_sha256":"8197c733a08495888f129f41f0f3c84303f638d29e4b9824e15ead3f95ddbe11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:01.536899Z","signature_b64":"wWHHtQGTybbQ+73ltIOCJMSKmI4XmGhKEC03LU+YhegS41fQ6GDk+akoriA0Azl5uhW5mTtYo34qLU1grRiRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8197c733a08495888f129f41f0f3c84303f638d29e4b9824e15ead3f95ddbe11","last_reissued_at":"2026-05-18T02:30:01.536377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:01.536377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0820","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWMLzzF4CIbqCye9nKMufBuPcFSGue29/QfZmemUFwtdyoedPvAVLn+BYe0oGup/wQpYcfvvUouOytOC6u6wCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:19:13.721385Z"},"content_sha256":"4760ea1210718453899ce2867f1c2969ab64993af059d8302cea0f360b292fcf","schema_version":"1.0","event_id":"sha256:4760ea1210718453899ce2867f1c2969ab64993af059d8302cea0f360b292fcf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QGL4OM5AQSKYRDYST5A7B46IIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jae-Hoon Kwon","submitted_at":"2010-07-06T07:11:07Z","abstract_excerpt":"We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A_{+\\infty}$, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers the Sagan and Stanley's corres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0820","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9E5kFUg6ekKuYzCcoQpQij5uFU0eJWLBw5YqFtmEG4nNeyw32nvgR/o73MVm/7LW/6KcmnZw6/NNZEyFIV9IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:19:13.721988Z"},"content_sha256":"144ceff77f4f185d0582b997fe10e58d393a6c74bee8278fbef51d34d6ea2822","schema_version":"1.0","event_id":"sha256:144ceff77f4f185d0582b997fe10e58d393a6c74bee8278fbef51d34d6ea2822"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QGL4OM5AQSKYRDYST5A7B46IIM/bundle.json","state_url":"https://pith.science/pith/QGL4OM5AQSKYRDYST5A7B46IIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QGL4OM5AQSKYRDYST5A7B46IIM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T14:19:13Z","links":{"resolver":"https://pith.science/pith/QGL4OM5AQSKYRDYST5A7B46IIM","bundle":"https://pith.science/pith/QGL4OM5AQSKYRDYST5A7B46IIM/bundle.json","state":"https://pith.science/pith/QGL4OM5AQSKYRDYST5A7B46IIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QGL4OM5AQSKYRDYST5A7B46IIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QGL4OM5AQSKYRDYST5A7B46IIM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fa513de4d0e54af60d43cfe06c1cf8b7c60c3bca38c85c4a3893bc46e2ff4726","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T07:11:07Z","title_canon_sha256":"fa192292920f6a34e10250a75b4208883ebec66c151db7d9202794969febe5cc"},"schema_version":"1.0","source":{"id":"1007.0820","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0820","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0820v1","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0820","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"QGL4OM5AQSKY","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QGL4OM5AQSKYRDYS","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QGL4OM5A","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:144ceff77f4f185d0582b997fe10e58d393a6c74bee8278fbef51d34d6ea2822","target":"graph","created_at":"2026-05-18T02:30:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A_{+\\infty}$, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers the Sagan and Stanley's corres","authors_text":"Jae-Hoon Kwon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T07:11:07Z","title":"A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0820","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4760ea1210718453899ce2867f1c2969ab64993af059d8302cea0f360b292fcf","target":"record","created_at":"2026-05-18T02:30:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fa513de4d0e54af60d43cfe06c1cf8b7c60c3bca38c85c4a3893bc46e2ff4726","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-07-06T07:11:07Z","title_canon_sha256":"fa192292920f6a34e10250a75b4208883ebec66c151db7d9202794969febe5cc"},"schema_version":"1.0","source":{"id":"1007.0820","kind":"arxiv","version":1}},"canonical_sha256":"8197c733a08495888f129f41f0f3c84303f638d29e4b9824e15ead3f95ddbe11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8197c733a08495888f129f41f0f3c84303f638d29e4b9824e15ead3f95ddbe11","first_computed_at":"2026-05-18T02:30:01.536377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:01.536377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wWHHtQGTybbQ+73ltIOCJMSKmI4XmGhKEC03LU+YhegS41fQ6GDk+akoriA0Azl5uhW5mTtYo34qLU1grRiRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:01.536899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4760ea1210718453899ce2867f1c2969ab64993af059d8302cea0f360b292fcf","sha256:144ceff77f4f185d0582b997fe10e58d393a6c74bee8278fbef51d34d6ea2822"],"state_sha256":"baeddb8ad2b8b774706081f913d848e0d8913864a914e8b324c90e16fa312326"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jcDtjDo5TgEdxPyjkxtQKKdZoEc7Y3gKpbBAdZK8maNGaVFppxoFPvCW0QRZ+vQMsS6qx0vneqYHIYaRe08vBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:19:13.724983Z","bundle_sha256":"aa696a554a15c784ab078c83b4bb5eceefcef3deaf4a8db4000eaaf06216f5f5"}}